Single-crystal X-ray diffraction study of novel pyrazole chalcone derived from 1-phenyl-3-p-tolyl-1H-pyrazole-4-carbaldehyde

143-146Novel pyrazole chalcone has been synthesized by reaction of phenyl-3-p-tolyl-1H-pyrazole-4-carbaldehyde and acetophenone by Claisen-Schmidt reaction in ethanol by microwave assisted method. It has been characterized by elemental analysis and spectroscopic (FTIR, 1H NMR and MS) studies. Crystal structure of the compound has been determined using single-crystal X-ray diffraction. Hydrogen-bonded chain is formed by C–H···O bonding enhanced by C–H···π interaction. Adjacent chains are connected through the π∙∙∙π interactions

Approximation of holomorphic mappings on strongly pseudoconvex domains

Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We prove that the set A(D,Y), consisting of all continuous maps from the closure of D to Y which are holomorphic in D, is a complex Banach manifold. When D is the unit disc in C (or any other topologically trivial strongly pseudoconvex domain in a Stein manifold), A(D,Y) is locally modeled on the Banach space A(D,C^n)=A(D)^n with n=dim Y. Analogous results hold for maps which are holomorphic in D and of class C^r up to the boundary for any positive integer r. We also establish the Oka property for sections of continuous or smooth fiber bundles over the closure of D which are holomorphic over D and whose fiber enjoys the Convex approximation property. The main analytic technique used in the paper is a method of gluing holomorphic sprays over Cartan pairs in Stein manifolds, with control up to the boundary, which was developed in our paper "Holomorphic curves in complex manifolds" (Duke Math. J. 139 (2007), no. 2, 203--253)

Study of solid state structural and bonding features of (E)-1-(4-bromophenyl)-3-(1-H-indol-3-yl)-prop-2-en-1-one

1211-1214Single-crystal study of indolyl chalcone (E)-1-(4-bromophenyl)-3-(1-H-indol-3-yl)-prop-2-en-1-one is reported here. It has been synthesized by microwave assisted method from indole-3-carbaldehyde and 4-bromo acetophenone by Claisen-Schmidt reaction. IR,1H NMR and HRMS data is reported here. The crystalline structure of this compound is described within the sp. gr. I -4; its unit cell parameters are a = 23.9636(17)Å,b = 23.9636(17)Å,c = 5.1428(5)Å. Crystallographic study shows formation of hydrogen-bonded cyclic tetramer around a 2-fold axis and 4-fold roto-inversion axis through N1–H1···O1 interactions between the indolic NH group as a hydrogen-bond donor and the carbonyl O atom as a hydrogen-bond acceptor

A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

An interpolation theorem for proper holomorphic embeddings

Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster

Probing seed black holes using future gravitational-wave detectors

Identifying the properties of the first generation of seeds of massive black holes is key to understanding the merger history and growth of galaxies. Mergers between ~100 solar mass seed black holes generate gravitational waves in the 0.1-10Hz band that lies between the sensitivity bands of existing ground-based detectors and the planned space-based gravitational wave detector, the Laser Interferometer Space Antenna (LISA). However, there are proposals for more advanced detectors that will bridge this gap, including the third generation ground-based Einstein Telescope and the space-based detector DECIGO. In this paper we demonstrate that such future detectors should be able to detect gravitational waves produced by the coalescence of the first generation of light seed black-hole binaries and provide information on the evolution of structure in that era. These observations will be complementary to those that LISA will make of subsequent mergers between more massive black holes. We compute the sensitivity of various future detectors to seed black-hole mergers, and use this to explore the number and properties of the events that each detector might see in three years of observation. For this calculation, we make use of galaxy merger trees and two different seed black hole mass distributions in order to construct the astrophysical population of events. We also consider the accuracy with which networks of future ground-based detectors will be able to measure the parameters of seed black hole mergers, in particular the luminosity distance to the source. We show that distance precisions of ~30% are achievable, which should be sufficient for us to say with confidence that the sources are at high redshift.Comment: 14 pages, 6 figures, 2 tables, accepted for proceedings of 13th GWDAW meetin

Do diurnal cortisol levels mediate the association between sleep disturbances and cognitive impairment?

Previous research found an association between sleep disturbances and cognitive deficits on the one hand, and between increased cortisol levels and poor cognitive performance on the other hand. We hypothesized that cortisol may, at least partially, mediate the link between sleep disturbances and cognitive impairment (CI). We analyzed data from 440 nondemented subjects aged ≥65 years (72.4 ± 4.5 years old, 55.7% women) participating at the population-based CoLaus/PsyCoLaus study, who underwent cognitive evaluation, complete polysomnography and cortisol measures during the day. Subjects with CI (N = 207, 47.05% of the sample) had lower sleep efficiency, less deep sleep (stage N3) and rapid eye movement sleep, and higher apnea/hypopnea index and oxygen desaturation index. After adjustment for possible confounders, oxygen desaturation index (≥4% and ≥6% per hour of sleep) were significantly associated with impaired cognitive performance. The results of Sobel's test for mediation using the regressions between the sleep-related variables and cortisol values, and between the cortisol and the Clinical Dementia Rating score were not significant (all p > 0.05). Our data suggest that sleep-disordered breathing is associated with CI, but that this association is not mediated by increased diurnal cortisol levels

Sensitivity Studies for Third-Generation Gravitational Wave Observatories

Advanced gravitational wave detectors, currently under construction, are expected to directly observe gravitational wave signals of astrophysical origin. The Einstein Telescope, a third-generation gravitational wave detector, has been proposed in order to fully open up the emerging field of gravitational wave astronomy. In this article we describe sensitivity models for the Einstein Telescope and investigate potential limits imposed by fundamental noise sources. A special focus is set on evaluating the frequency band below 10Hz where a complex mixture of seismic, gravity gradient, suspension thermal and radiation pressure noise dominates. We develop the most accurate sensitivity model, referred to as ET-D, for a third-generation detector so far, including the most relevant fundamental noise contributions.Comment: 13 pages, 7 picture